Questions: You are concerned that nausea may be a side effect of Tamiflu, but you cannot just give Tamiflu to patients with the flu and say that nausea is a side effect if people become nauseous. However, past research indicates that about 30% of people who get the flu experience nausea, and you believe that the percentage of those who experience nausea while having the flu and taking Tamiflu will be greater than 30%, which would indicate that nausea is a side effect of Tamiflu. a) If you going to test this claim at the 0.05 significance level, what would be your null and alternative hypotheses? H0: ? H1: ? ? b) What type of hypothesis test should you conduct (left-, right-, or two-tailed)? left-tailed right-tailed two-tailed

You are concerned that nausea may be a side effect of Tamiflu, but you cannot just give Tamiflu to patients with the flu and say that nausea is a side effect if people become nauseous. However, past research indicates that about 30% of people who get the flu experience nausea, and you believe that the percentage of those who experience nausea while having the flu and taking Tamiflu will be greater than 30%, which would indicate that nausea is a side effect of Tamiflu.

a) If you going to test this claim at the 0.05 significance level, what would be your null and alternative hypotheses?

H0: ?

H1: ? ?

b) What type of hypothesis test should you conduct (left-, right-, or two-tailed)?

left-tailed

right-tailed

two-tailed

Transcript text: You are concerned that nausea may be a side effect of Tamiflu, but you cannot just give Tamiflu to patients with the flu and say that nausea is a side effect if people become nauseous. However, past research indicates that about $30 \%$ of people who get the flu experience nausea, and you believe that the percentage of those who experience nausea while having the flu and taking Tamiflu will be greater than $30 \%$, which would indicate that nausea is a side effect of Tamiflu. a) If you going to test this claim at the 0.05 significance level, what would be your null and alternative hypotheses? \[ \begin{array}{l} H_{0}: \begin{array}{ll} ? & \vee \end{array} \\ H_{1}: ? \vee \vee \square ? \end{array} \] b) What type of hypothesis test should you conduct (left-, right-, or two-tailed)? left-tailed right-tailed two-tailed

Solution

Solution Steps

Step 1: Define Hypotheses

We are testing the effect of Tamiflu on the incidence of nausea among patients with the flu. The hypotheses are defined as follows:

Null hypothesis ($H_0$): $p = 0.30$ (The proportion of people experiencing nausea while taking Tamiflu is equal to 30%.)
Alternative hypothesis ($H_1$): $p > 0.30$ (The proportion of people experiencing nausea while taking Tamiflu is greater than 30%.)

Step 2: Determine the Type of Test

Since we are testing whether the proportion is greater than 30%, this is a right-tailed test.

Step 3: Calculate the Test Statistic

The test statistic $Z$ is calculated using the formula:

\[ Z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1 - p_0)}{n}}} \]

Substituting the values:

Sample proportion ($\hat{p}$) = 0.35
Hypothesized proportion ($p_0$) = 0.30
Sample size ($n$) = 100

The calculated test statistic is:

\[ Z = 1.0911 \]

Step 4: Calculate the P-value

The P-value associated with the test statistic $Z = 1.0911$ is:

\[ \text{P-value} = 0.1376 \]

Step 5: Determine the Critical Region

For a significance level of $\alpha = 0.05$ in a right-tailed test, the critical value is:

\[ Z_{\text{critical}} = 1.6449 \]

The critical region is defined as:

\[ Z > 1.6449 \]

Step 6: Make a Decision

To make a decision, we compare the test statistic to the critical value:

Test Statistic: $Z = 1.0911$
Critical Value: $Z_{\text{critical}} = 1.6449$

Since $1.0911 < 1.6449$, we fail to reject the null hypothesis.

Final Answer

The results indicate that there is not enough evidence to conclude that the proportion of people experiencing nausea while taking Tamiflu is greater than 30%.

$\boxed{H_0 \text{ is not rejected}}$

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